Geometry: Triangles
Classifying triangles and using angle relationships
Geometry: Triangles
Classifying triangles and using angle relationships
Geometry - Grade 6-8
- 1
A triangle has angle measures of 40 degrees, 60 degrees, and 80 degrees. Classify the triangle by its angles.
Compare each angle measure to 90 degrees.
The triangle is an acute triangle because all three angles are less than 90 degrees. - 2
A triangle has side lengths of 6 cm, 6 cm, and 9 cm. Classify the triangle by its sides.
The triangle is isosceles because it has exactly two sides with the same length. - 3
Two angles of a triangle measure 35 degrees and 75 degrees. Find the measure of the third angle.
The sum of the interior angles of every triangle is 180 degrees.
The third angle measures 70 degrees because the angles in a triangle add to 180 degrees, and 180 - 35 - 75 = 70. - 4
A triangle has angle measures of 90 degrees, 30 degrees, and 60 degrees. Classify the triangle by its angles and by its sides if all side lengths are different.
The triangle is a right triangle because it has one 90 degree angle. It is also scalene because all three side lengths are different. - 5
Can side lengths of 4 cm, 7 cm, and 12 cm form a triangle? Explain your answer.
Use the triangle inequality rule.
No, these side lengths cannot form a triangle because 4 + 7 = 11, and 11 is not greater than 12. The sum of the two shorter sides must be greater than the longest side. - 6
In triangle ABC, angle A measures 50 degrees and angle B measures 65 degrees. What is the measure of angle C?
Angle C measures 65 degrees because 180 - 50 - 65 = 65. - 7
A triangle has side lengths of 8 units, 8 units, and 8 units. Classify the triangle by its sides and explain what you know about its angles.
Equal sides in a triangle are across from equal angles.
The triangle is equilateral because all three sides are equal. Each angle measures 60 degrees because an equilateral triangle has three equal angles that add to 180 degrees. - 8
A triangle has one angle that measures 115 degrees. What type of triangle is it by its angles?
The triangle is obtuse because it has one angle greater than 90 degrees. - 9
Find the value of x in a triangle with angles measuring x degrees, 45 degrees, and 55 degrees.
Set up an equation using the triangle angle sum.
The value of x is 80 because x + 45 + 55 = 180, so x + 100 = 180 and x = 80. - 10
A triangle has side lengths of 5 inches, 12 inches, and 13 inches. Does it appear to be a right triangle? Use the Pythagorean relationship to explain.
Yes, it is a right triangle because 5 squared plus 12 squared equals 13 squared. Since 25 + 144 = 169, the side lengths satisfy the Pythagorean relationship. - 11
In the diagram, a triangle has two equal sides. The angle between the equal sides measures 40 degrees. What are the measures of the other two angles?
In an isosceles triangle, the angles opposite the equal sides are equal.
The other two angles each measure 70 degrees. The triangle is isosceles, so the two base angles are equal, and 180 - 40 = 140, then 140 divided by 2 = 70. - 12
The exterior angle of a triangle measures 120 degrees. The two remote interior angles are labeled 45 degrees and x degrees. Find x.
Use the exterior angle theorem.
The value of x is 75 degrees because an exterior angle equals the sum of the two remote interior angles, so 45 + x = 120 and x = 75. - 13
Can a triangle have angle measures of 25 degrees, 65 degrees, and 100 degrees? Explain your answer.
No, these cannot be the angle measures of a triangle because 25 + 65 + 100 = 190, and the angles in a triangle must add to 180 degrees. - 14
A scalene triangle has sides labeled 7 cm, 10 cm, and 12 cm. Which angle is the largest: the angle opposite 7 cm, the angle opposite 10 cm, or the angle opposite 12 cm?
Longer sides are opposite larger angles.
The angle opposite 12 cm is the largest because the largest angle in a triangle is always across from the longest side. - 15
A triangle is shown with angles labeled 2x degrees, 3x degrees, and 4x degrees. Find the value of x and the measure of each angle.
The value of x is 20 because 2x + 3x + 4x = 180, so 9x = 180 and x = 20. The angle measures are 40 degrees, 60 degrees, and 80 degrees.